In document imaging systems, integrating cavity effect (ICE) is defined as the increase in perceived reflectance of the imaged portion of a document done due to the reflectance of the surrounding portion of that document. The illuminator kernel function, or one trip spread function (OTSF), characterizes the ICE present during an imaging operation. Insight into the functional form of the OTSF of a complex system can be gained from an analysis of the OTSF of simpler, related systems. Closed form expressions for the OTSF of a simple strip illumination system are derived. These expressions are shown to be a good approximation to the exact OTSF of this system by comparison to Monte Carlo- based illumination ray tracing results. Using the closed form expressions one can easily calculate the approximate magnitude of ICE present in similar systems.